Stability Analysis of a Simplified Yet Complete Model for Chronic Myelegenous Leukemia

TL;DR

This paper investigates a simplified PDE model for hematopoiesis and chronic myelogenous leukemia, demonstrating its stability and similarity to more complex models, thus aiding understanding and comparison with experimental data.

Contribution

The paper introduces a simplified PDE model derived from an agent-based model, enabling easier analysis and comparison while maintaining key dynamic properties.

Findings

Simplified PDE model exhibits similar stability properties to the original agent-based model.

Numerical simulations justify the approximations made in the simplified model.

The model's fewer parameters facilitate comparison with experimental data.

Abstract

We analyze the asymptotic behavior of a partial differential equation (PDE) model for hematopoiesis. This PDE model is derived from the original agent-based model formulated by (Roeder et al., Nat. Med., 2006), and it describes the progression of blood cell development from the stem cell to the terminally differentiated state. To conduct our analysis, we start with the PDE model of (Kim et al, JTB, 2007), which coincides very well with the simulation results obtained by Roeder et al. We simplify the PDE model to make it amenable to analysis and justify our approximations using numerical simulations. An analysis of the simplified PDE model proves to exhibit very similar properties to those of the original agent-based model, even if for slightly different parameters. Hence, the simplified model is of value in understanding the dynamics of hematopoiesis and of chronic myelogenous leukemia, and it presents the advantage of having fewer parameters, which makes comparison with both experimental data and alternative models much easier.